In semiconductor fabrication processes, the resolution of a photoresist pattern begins to blur at about 45 nanometer (nm) half pitch. To continue to use fabrication equipment purchased for larger technology nodes, double exposure methods have been developed.
Double exposure involves forming patterns on a single layer of a substrate using two different masks in succession. As a result, a minimum line spacing in the combined pattern can be reduced while maintaining good resolution. In a method referred to as double dipole lithography (DDL), the patterns to be formed on the layer are decomposed and formed on a first mask having only horizontal lines, and on a second mask having only vertical lines. The first and second masks are said to have 1-dimensional (1-D) patterns, which can be printed with existing lithographic tools.
Another form of double exposure is referred to as double patterning technology (DPT). Unlike the 1-D approach of DDL, DPT in some cases allows a vertex (angle) to be formed of a vertical segment and a horizontal segment on the same mask. Thus, DPT generally allows for greater reduction in overall IC layout than DDL does. DPT is a layout splitting method analogous to a two coloring problem for layout splitting in graph theory. The layout polygon and critical space are similar to the vertex and edge of the graph respectively. Two adjacent vertices connected with an edge should be assigned different colors. If only two masks are to be used, then only two “color types” are assigned. Each pattern on the layer is assigned a first or second “color”; the patterns of the first color are formed by a first mask, and the patterns of the second color are formed by a second mask. A graph is 2-colorable only if it contains no odd loop.
In terms of graph theory, when the total number of relationships between patterns that violate the minimum threshold spacing for a single mask (referred to as the separator distance) is odd, an odd loop is present, and DPT cannot be used without changing the layout.
In some cases, after a layout has proceeded through double patterning decomposition, and photomasks are produced, the designer discovers an underlying logic error in the design, which must be corrected through a design change (e.g., an engineering change order). Such a design change may require new photomasks, at added expense. Because two masks are used for a single layer, the added expense is doubled.